Problem: Which of the following numbers is a factor of 165? ${2,7,11,12,13}$
Solution: By definition, a factor of a number will divide evenly into that number. We can start by dividing $165$ by each of our answer choices. $165 \div 2 = 82\text{ R }1$ $165 \div 7 = 23\text{ R }4$ $165 \div 11 = 15$ $165 \div 12 = 13\text{ R }9$ $165 \div 13 = 12\text{ R }9$ The only answer choice that divides into $165$ with no remainder is $11$ $ 15$ $11$ $165$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $11$ are contained within the prime factors of $165$ $165 = 3\times5\times11 11 = 11$ Therefore the only factor of $165$ out of our choices is $11$. We can say that $165$ is divisible by $11$.